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How to make an enemy chase player, using collisions

Player is a FirstPersonController running around on a terrain. I want the enemies to be similar, they just look at and move toward the player, reacting to the terrain in much the same way as the player.

I got the enemy chasing the player using it's transform.LookAt and transform.Translate but of course it moves in 3D space rather than along the ground.

So how is this achieved? I assumed using the rigidbody.velocity but none of the myriad of things I tried worked.